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A336365 Rectangular array by antidiagonals: row n shows the nonnegative integers whose distance to the nearest prime is n.

%I A336365 #5 Aug 17 2020 06:40:52
%S A336365 2,3,1,5,4,0,7,6,9,26,11,8,15,34,93,13,10,21,50,117,118,17,12,25,56,
%T A336365 123,122,119,19,14,27,64,143,144,121,120,23,16,33,76,145,186,205,300,
%U A336365 531,29,18,35,86,185,204,217,324,533,532,31,20,39,92,187,206
%N A336365 Rectangular array by antidiagonals: row n shows the nonnegative integers whose distance to the nearest prime is n.
%C A336365 Row 1: the primes, A000040.
%C A336365 Every nonnegative integer occurs exactly once, so that as a sequence, this is a permutation of the nonnegative integers.
%e A336365  Corner:
%e A336365    2    3    5    7   11   13   17   19   23   29   31   37
%e A336365    1    4    6    8   10   12   14   16   18   20   22   24
%e A336365    0    9   15   21   24   27   33   35   39   45   49   51
%e A336365   26   34   50   56   64   76   86   92   94  116  124  134
%e A336365   93  117  123  143  145  185  187  203  207  215  219  245
%t A336365 a[_?PrimeQ] = 0; a[n_] := Min[NextPrime[n] - n, n - NextPrime[n, -1]];
%t A336365 t = Table[a[n], {n, 0, 2000}]; (*  A051699 *)
%t A336365 r[n_] := -1 + Flatten[Position[t, n]]; u[n_, k_] := r[n][[k]];
%t A336365 TableForm[Table[u[n, k], {n, 0, 15}, {k, 1, Length[r[n]]}]] (* A336365, array *)
%t A336365 Table[u[n - k, k], {n, 0, 15}, {k, n, 1, -1}] // Flatten  (* A336365, sequence *)
%Y A336365 Cf. A000040, A051699, A336364.
%K A336365 nonn,tabl
%O A336365 1,1
%A A336365 _Clark Kimberling_, Jul 19 2020